Control Theory and Informatics                                                                 www.iiste.orgISSN 2224-5774...
Control Theory and Informatics                                                                         www.iiste.orgISSN 2...
Control Theory and Informatics                                                                    www.iiste.orgISSN 2224-5...
Control Theory and Informatics                                                           www.iiste.orgISSN 2224-5774 (prin...
Control Theory and Informatics                                                           www.iiste.orgISSN 2224-5774 (prin...
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1.[1 5]implementation of pre compensation fuzzy for a cascade pid controller using matlab simulink


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1.[1 5]implementation of pre compensation fuzzy for a cascade pid controller using matlab simulink

  1. 1. Control Theory and Informatics www.iiste.orgISSN 2224-5774 (print) ISSN 2225-0492 (online)Vol 1, No.1, 2011 Implementation of Pre Compensation Fuzzy For a Cascade PID Controller Using Matlab Simulink Anilkumar Bethapudi Dept of E.I.E, AITAM, Tekkali-532201, Andhra Pradesh, India. E-mail: G..S.S.S.S.V. Krishna Mohan Dept of E.I.E, AITAM, Tekkali-532201, Andhra Pradesh, India. E-mail: g_k_mohan@yahoo.comAbstract:Fuzzy logic control technology has been widely and successfully utilized in numerous industrial applications.Since fuzzy logic with humanlike but systematic properties can convert linguistic control rule based on expertknowledge into automatic control strategies, it can be well applied to control the process with un modeled andnonlinear dynamics. In this paper a fuzzy logic based pre compensation scheme for PID controller is proposed.Fuzzy methods can be used effectively to implement conventional control methods for performanceimprovement. The scheme is based on graphically studying the source of steady state errors arising fromapplying PID type schemes of systems with dead zones. This work is based on trying to compensate forovershoot and undershoot by the transient response. This is easy to implement in practice since an existing PIDcontroller can be used in conjunction with the fuzzy pre compensator without modificationKeywords: Fuzzy controller, PID Controller ,Fuzzification, Defuzzification.1. Introduction PID controllers are widely used in process industries to control various processes.PID controllerapplicability is for linear process. PID controller produces a poor response for large load disturbances. Thereforeproper tuning is necessary to the controller to give a satisfactory response. To overcome these disadvantages wepropose a scheme called fuzzy pre compensator for a PID controller.1.1 Advantages of fuzzy pre compensator No need for precise tuning. It reduces 90% of overshoot which occur in the PID controller. It acts as an adaptive controller. It has faster settling time.1.2. Disadvantage of fuzzy pre compensatorThe complexity involved in forming the fuzzy membership function is to be considered.2. Fuzzy Precompensated PID Controller2.1 Control structureFigure.1 illustrates the basic control structure. The scheme consists of a conventional PID control structuretogether with the proposed fuzzy pre compensator.The pre compensator uses the command input ym and the plant output yp to generate a pre compensatedcommand output y1 m described by the following equations ∆e( k ) = e( k ) - e( k-1) ………….……………(2) γ( k ) = F[ e( k ), ∆ e( k ) ] ………. …………(3) y1m ( k ) = ym (k) + γ( k ). ……...………………..(4) In the above, e( k ) is the tracking error between the command input ym(k) and the plant output yp(k),and e( k ) is the change in the tracking error. The term F[e(k),e( k )] is a nonlinear mapping of e( k ) and ∆1|
  2. 2. Control Theory and Informatics www.iiste.orgISSN 2224-5774 (print) ISSN 2225-0492 (online)Vol 1, No.1, 2011e( k )based on fuzzy logic described below. The term γ ( k ) = F[ e( k ),∆e( k ) ] represents pre compensation orcorrection term so that the compensated command signaly1m( k ) is simply the sum of the external commandsignal ym (k) and γ ( k). The correction term is based on the error e( k ) and ∆ e( k ). The compensated commandsignal y1m( k ) is applied to a conventional PID controller as shown in figure 1.a The equations determining thePI controller are as follows. e1( k ) = y1m (k) - y(k)………………..…..(5) ∆ e1( k ) = e1 ( k ) - e1 ( k-1)…………...........(6) u (k) = u(k-1) +Kp ∆ e1( k ) +K1 e1( k )..(7) The quantity e1(k) is the pre compensated tracking error of the pre compensated command input y1 m(k) and the plant output yp(k), and ∆ e1( k ) is the change in the pre compensated tracking error. The control u(k) is applied to the input of the plant. The purpose of the fuzzy pre compensator is to modify the command signal to compensate forovershoots and undershoots present in the output response when the plant has unknown nonlinearities. Suchnonlinearities can result in significant overshoots and undershoots if a conventional PID control scheme is used.The pre compensator uses fuzzy logic rules that are based on the above motivation.3.Fuzzy precompensater The implementation of the fuzzy logic based term is γ ( k ) = F[ e( k ), ∆ e( k ) ]. .In the descriptionstandard terminology is used to form fuzzy set theory, for a treatment of fuzzy sets, e( k ), and ∆ e( k) as inputsto the map F, and γ ( k ) as the output. Associated with the map F is a collection of linguistic values, L= {NB, NM, NS, ZO, PS, PM, PB}these values represent the term set for the input and output variables of F. In this case seven linguistic values areused. The meaning of each linguistic value in the term set L should be clear from its mnemonic; for example,NB stands for negative big, NM for negative medium, NS for negative small, ZO for zero and likewise for thepositive (p) linguistic value. Associated with the term set L is a collection of membership functions. µ = { µ NB, µNM, µNS, µ ZO, µPS, µPM, µ PB }Each membership function is a map from the real line to the interval [-1 +1]. Figure .2a shows a plot of themembership functions. In this application the MF used is the triangular type. The height of the MF in this case isone, which occurs at the points –1, -0.4,-0.25,0 0.25,0.4,1 respectively.The realization of the function F [e (k), ∆ e (k)] deals into the setting of linguistic values. This consists ofscaling the inputs e (k) and ∆ e(k) appropriately and then converting them into fuzzy sets. The symbol Ce for thescaling constant for the input e (k) and the symbol C∆e for the scaling constant for the input ∆ e (k). For eachlinguistic value l∈ L, assign a pair of numbers ne(l) and n∆e(l) to the inputs e( k ) and ∆ e( k ) via the associatedmembership function ne(l) = µl (Ce e( k ) ) …………….. (8) n∆e(l) = µl (C∆e ∆ e( k ) ) …………..(9)The numbers ne(l) and n∆e(l), l L are used in the computation of F[ e( k ), ∆ e( k ) ].4. Decision making process Associated with the decision making process is a set of fuzzy rules R = {R1, R2…Rr}, where r is thetotal number of rules. Each RI, I = 1,2,3,...r, is represented by a triplet ( li ∆, li ∆c, li γ ), where li ∆, li ∆c, li γ L.2|
  3. 3. Control Theory and Informatics www.iiste.orgISSN 2224-5774 (print) ISSN 2225-0492 (online)Vol 1, No.1, 2011The first two linguistic values are associated with the input variables e( k ), and ∆ e( k ) while the third linguisticvalue is associated with the output. An example of a rule is the triplet (NS,PS,ZO).Rules are often written in theform: “if e( k ) is le and ∆e( k ) is l ∆e then γ is lγ “.For example, in the rule represented by the triplet(ZO,NS,NM), the idea of the rule is that if e( k ) is zero and ∆e( k ) is negative small, then output is negativemedium. The set of rules used in this fuzzy pre compensator is given in table 1. There are 47 rules. These rules are derived by using a combination of experience, trial and error and the knowledge of theresponse of the system. These are common approaches to the design of fuzzy logic rules as.To explain how these rules were obtained, consider for example the rule (ZO,NM,NM) in table1.Suppose the command signal is a constant ym, the error e(k) is zero and the change of error ∆e( k ) is negativenumber. This means that the output yp (k) is increasing, i.e, heading in the direction of an overshoot. To compensate for this, the command signal is to be decrease. This corresponds to applying acorrection term γ(k) as negative. Hence rule “if error is zero and change of error is negative medium, then outputis negative medium, correction term”. Similarly all rules are made.5. Defuzzification stage Defuzzification strategy is a mapping from a space of fuzzy control actions defined over an outputuniverse of discourse into a space of no fuzzy control actions. It is employed because in practical applications acrisp action is required. It is aimed at producing a non-fuzzy control action. However, in this part center of areadefuzzification is applied. γ(K) = ∫ µ ≤ ( γ)γdγ x Cγ ................ (10) µ ≤ ( γ)dγWhere ∫ denotes algebraic integrationFunction of γ is also selected as triangular shape function as shown in the figure 2.c since the output signal isnormalized to the range from –1 to +1 the output command will exit and absolute value.6. ConclusionThe design methodology of fuzzy pre compensator and fuzzy rules for cascade PID controller were discussed,also the performance of the fuzzy pre compensator for a cascade PID control is tested by using matlab simulinkas shown in figure 1.b.7. Results and discussionThe Performance of PID Controller and FPC Controller (Simulation)By comparing the results from figure3 we can conclude that the response obtained using FPC (Fuzzy PreCompensator) controller is better than the conventional PID controller. Even if the process parameter changesthe FPC controller adapts itself and produces good response. Hence it acts as an adaptive controller.We observed that conventional PID controller is not able to follow the set point but FPC controller follows theset point. The conventional PID controller gives a damped oscillation but FPC controller produces goodresponse. Hence FPC controller does not require precise tuning.ReferencesJong-Hwan Kim, Kwang-Choon Kim and Edwin K.P.Chong,"Fuzzy precompensated PID controllers", IEEETransactions on control system technologyVol.2, No.4, pp.406-411, December 1994.Y .Yasuda, S.L Mano and S.crotty , " A PID Controller with overshoots suppression Algorithm" in proc., of ISA ,90, ppI849-1872, October 1990C.C. Lee, "fuzzy logic control system: Fuzzy logic controller-part I, part II, IEEE Trans Syst. Man. Cybern.,vol.20, pp.405-415, January 1990R. C. Kavanagh, J. M. D. Murphy, and M. Egan, “Torque ripple mini-mization in switched reluctance drivesusing self learning techniques,” in Proc. IEEE IECON’91, 1991, pp. 289–294.S. Mir, M. E. Ebulbuk, and I. Husain, “Torque ripple minimization in switched reluctance motors using adaptive3|
  4. 4. Control Theory and Informatics www.iiste.orgISSN 2224-5774 (print) ISSN 2225-0492 (online)Vol 1, No.1, 2011fuzzy control,” IEEE Trans. Ind. Applicat., vol. 35, pp. 461–468, Mar./Apr. 1999 Figure 1.a: Basic Control Structure of Fuzzy Pre-compensator Cascade Control Figure 1.b : System implemented in Matlab Simulink Figure 2.a: Membership function of error (e)4|
  5. 5. Control Theory and Informatics www.iiste.orgISSN 2224-5774 (print) ISSN 2225-0492 (online)Vol 1, No.1, 2011 Figure 2b: Membership function of change in error (Δe) Figure 2.c: Membership function of Controller output (γ) Figure 3: Response of FPC and PID controller for varying Set point with continuous load disturbance Table 1.: DML rule table of the FLC ∆e NB NM NS ZO PS PM PB e NB NB NB NB NM NS NS ZO NM NB NB NM NS NS ZO PS NS NB NM NS NS ZO PS PM ZO NM NM NS ZO PS PM PM PS NM NS ZO PS PS PM PB PM NS ZO PS PS PM PB PB PB ZO PS PS PM PB PB PB5|